The subject disclosure relates to quantum circuits, e.g., quantum circuit design. Quantum computing employs quantum physics to encode and process information rather than binary digital techniques based on transistors. A quantum computing device employs quantum bits (also referred to as qubits) that operate according to the laws of quantum physics and can exhibit phenomena such as superposition and entanglement. The superposition principle of quantum physics allows qubits to be in a state that partially represent both a value of “1” and a value of “O” at the same time. The entanglement principle of quantum physics allows qubits to be correlated with each other such that the combined states of the qubits cannot be factored into individual qubit states. For instance, a state of a first qubit can depend on a state of a second qubit. As such, a quantum circuit can employ qubits to encode and process information in a manner that can be significantly different from binary digital techniques based on transistors. However, the designing of quantum circuits often can be relatively difficult and/or time consuming.
With regard to quantum circuit design, a conventional approach can be to employ a universal quantum computing circuit that can be utilized, with varying and/or limited levels of performance, for virtually all types of algorithms. A universal quantum computing circuit design can be utilized for an algorithm to create a superconducting quantum computing circuit to perform superconducting quantum circuit operations. A universal quantum computing circuit typically can have qubits that can be connected to all of their neighbor qubits, and typically can run all or virtually all types of algorithms, although with varying and/or limited levels of performance, due at least in part to, for example, resource limits and design constraints, as well as the universal nature of the connectivity of the qubits in the universal quantum computing circuit. With regard to universal quantum computing circuits, for operations on qubits that have no direct connection, multiple swap gates typically can be used. However, there can be a number of problems with using universal quantum computing circuits for algorithms, particularly with regard to using universal quantum computing circuits on non-ideal quantum processors. Certain quantum processors can be considered non-ideal, for example, because they can comprise non-ideal qubits (e.g., short coherence times) and/or non-ideal gates (e.g., gate errors). Due to these and/or other non-idealities, there can be a limit on the number of gate operations that can be employed while still obtaining reasonable fidelity of the final outcome. These types of circuits are often referred to as shallow. Universal quantum computing circuits can have a general connectivity onto which any algorithm, in principle, can be implemented. However, there can be an undesirable and/or unduly higher accumulative error rate when using a universal quantum computing circuit for an algorithm, due in part to the relatively higher number of gate operations used, as gate fidelity is not 100%. These and other deficiencies of conventional quantum computing circuit designs, such as universal quantum computing circuits, can result in inefficient and/or ineffective circuits and/or inefficient performance of a quantum circuit design.